Shock Reflection in Plane Symmetry

TL;DR

This paper addresses the complex free boundary problem of shock reflection in plane symmetry for a barotropic fluid, establishing local solutions and characterizing the reflected shock's position after reflection.

Contribution

It introduces a method to determine the state behind the reflected shock and handles the unknown shock location and thermodynamic state with minimal initial data.

Findings

Established local in time solutions post-reflection

Determined the position of the reflected shock in space-time

Addressed the free boundary problem with limited initial data

Abstract

We consider the problem of shock reflection on a solid wall in plane symmetry for a barotropic fluid. We establish a local in time solution after the point of reflection, thereby determining the state behind the reflected shock. The location of the reflected shock in space time being unknown the problem constitutes a free boundary problem. Furthermore, the quantity describing the thermodynamic state of the fluid along the wall being also unknown, complete data for the problem is only given in a single point, the reflection point.